Question

If the product of zeroes x^2-3kx+2k^2-1 is 7 then values of k are ____ and ____​

Answer 1

Answer:

2 or -2

Step-by-step explanation:

product of zeroes=c/a

(2k^2-1)/1=7

2k^2-1=7

2k^2=8

k^2=4

k=2 or -2

Answer 2

The values of k are 2 and -2.

Given:

• The quadratic polynomial ${x}^{2} - 3kx + 2 {k}^{2} - 1$
• If the product of zeros is 7.

To find:

• Find the value of k.

Solution:

Concept to be used:

If $\alpha \: and \: \beta$ are zeros of $\bf a {x}^{2} + bx + c$ then

1. $\alpha + \beta = - \frac{b}{a}$ and
2. $\alpha \beta = \frac{c}{a}$

Step 1:

Write the coefficient of polynomial.

$a = 1$

$b = - 3k$

and

$c = 2 {k}^{2} - 1$

So,

If $\alpha \: and \: \beta$ are the zeros of polynomial, then

$\alpha \beta = \frac{2 {k}^{2} - 1}{1}$

or

$7 = 2 {k}^{2} - 1$

Step 2:

Solve for k.

$2 {k}^{2} = 1+7$

or

$2 {k}^{2} = 8$

or

${k}^{2} = 4$

or

$\bf k = \pm \: 2$

Thus,

The values of k are 2 and -2.

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